This function uses a dumb search to find the minimum distance between a point (or many points) and an ellipse. It has controllable accuracy which may be reduced for faster computation.

*Update 12 Jan 2010: Rody Oldenhuis has submitted a version of this file (possibly only for versions >=Matlab 2009a) that works for general 3D ellipses and should be more efficient than this one. Please see acknowledgements below.

While reading your post I was reminded of a long and tedious hunt I recently did for an efficient algorithm to find the distance between two confocal ellipses. One of the things I came across was exactly this problem (point - ellipse), and I remembered I still had the code for it somewhere.

So, I brushed it a bit, and I've just posted it (I made an acknowledgement to you as well). I hope my code can help you out.

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Updates

08 Jan 2010

Fixed a bug in original file.

11 Jan 2010

Added a link to point to a file that has been uploaded in response to my original description, which said that there exists a more efficient method than this, but it has not been implemented yet.